title: Sparse reconstruction of correlated multichannel activity.
abstract: Parametric methods for modeling sinusoidal signals with line spectra have been studied for decades. In general, these methods start by representing each sinusoidal component by means of two complex exponential functions, thereby doubling the number of unknown parameters. Recently, a Hankel-plus-Toeplitz matrix pencil method was proposed which directly models sinusoidal signals with discrete spectral content. Compared to its counterpart, which uses a Hankel matrix pencil, it halves the required number of time-domain samples and reduces the size of the involved linear systems. The aim of this paper is twofold. Firstly, to show that this Hankel-plus-Toeplitz matrix pencil also applies to continuous spectra. Secondly, to explore its use in the reconstruction of real-life signals. Promising preliminary results in the reconstruction of correlated multichannel electroencephalographic (EEG) activity are presented. A principal component analysis preprocessing step is carried out to exploit the redundancy in the channel domain. Then the reduced signal representation is successfully reconstructed from fewer samples using the Hankel-plus-Toeplitz matrix pencil. The obtained results encourage the future development of this matrix pencil method along the lines of well-established spectral analysis methods.
authors.forename: Sem
authors.initials: S
authors.lastname: Peelman
authors.forename: Joachim
authors.initials: J
authors.lastname: Van der Herten
authors.forename: Maarten
authors.initials: M
authors.lastname: De Vos
authors.forename: Wen-Shin
authors.initials: WS
authors.lastname: Lee
authors.forename: Sabine
authors.initials: S
authors.lastname: Van Huffel
authors.forename: Annie
authors.initials: A
authors.lastname: Cuyt
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004569:Electroencephalography / Q000379:methods*; D006801:Humans; D008962:Models, Theoretical; D025341:Principal Component Analysis; D012815:Signal Processing, Computer-Assisted; D014741:Video Recording